Question

How do you simplify `(2t)^5`?

Answer 1

Use the power of a product rule that states: `(ab)x=a^xb^x`.
Therefore, `(2t)^5=2^5t^5=32t^5`

Explanation:

In your question the `2` was the `a`, the `t` was the `b` and the `5` was the `x`.

Lets verify using 3 as x
`(2(3))^5 = 32(3)^5`
`6^5=32(243)`
`7776=7776`
It works out!

The power of a product rule works for any product and power.
Another example of the product of a power rule is as follows:
`(4tx)^3 = 4^3t^3x^3 = 64t^3x^3`

I hope you understand power of a product now.